While the presumptive allergic reaction is not unreasonable, there are two things that argue against this having been caused by minocycline: first, it very rarely causes allergic reactions; second, the lateness of the onset of the rash. While the latter does sometimes happen with allergic reactions (cumulative effect), it is exceptionally rare in antibiotic use, and especially in the tetracycline family. For that reason I'm suspecting this was coincidental.
What you might do before resuming minocycline therapy (if you even want to try, and it is a mystery as to why, but it's the one medication that seems to work on this particular problem) would be to take a few doses (spaced appropriately, not all at once) of an antihistimine, then start the minocycline. After that, try discontinuing the antihistamine. If the rash recurs then, you can assume it is, in fact, being caused by minocycline, and you will know you have something you can use to prevent this reaction. While some of the most effective antihistimines are those that cause the greatest drowsiness, there are some that work better with less of this (and some people don't have this happen as much as others, so you could get lucky). Benadryl would be the first choice except that it almost universally causes drowsiness. Zyrtec is also pretty broadly effective and doesn't generally cause such severe drowsiness, if at all.
This is my best advice overall. I do suspect the hives outbreak was due to something else based on the good record of the tetracyclines in this respect. However, it's not impossible, so if you'd like you could try one of the over-the-counter antihistimines in advance of resuming the monocycline. I hope this is helpful to you. Please follow up with us here as needed.
John Kenyon, EMT, CCT
Non-invasive cardiology tech, Emergency and Critical Care technician, Critical Incident Stress Mgmt. specialist